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The Mississippi Republican Party has certified election results naming incumbent Thad Cochran the winner of a U.S. Senate primary runoff that his Tea Party-backed challenger contends was tainted by illegal voting by Democrats.

Cochran defeated state Senator Chris McDaniel by 7,667 votes in the June 24 runoff, nearly 1,000 more than the six-term incumbent's unofficial margin of victory reported on election night, according to certified results released late on Monday by the state Republican Party.

Representatives from both campaigns sorted through voting records in all 82 Mississippi counties on Monday.

The party certification of the election left McDaniel weighing a possible challenge. His campaign said it had found thousands of cases of voters casting ballots in the Democratic primary and then in the Republican runoff, which is against election rules.

It has also highlighted unsubstantiated allegations that some Democrats - many of whom are black - were paid to vote for Cochran.

"We have a duty to look into those allegations to make sure the integrity of the process is upheld," said Michael Watson, a Republican state senator and legal adviser to the McDaniel campaign.

The Cochran campaign has dismissed allegations of vote buying on its part as false, but acknowledged on Tuesday it had erroneously listed in federal election filings roughly $53,000 in get-out-the vote payouts to dozens of workers as reimbursement to a single campaign staffer.

The Cochran campaign has also characterized allegations of improper voting as heavily overstated. It said in a statement that an initial review had turned up just over 200 questionable votes and 24 ineligible crossover votes.

Republican U.S. Senator Ted Cruz of Texas, another favorite of the conservative Tea Party movement, called on Monday for an official investigation into the runoff.

If McDaniel chooses to fight the results, he must first challenge them with the state Republican Party, said Pamela Weaver, spokeswoman for the Mississippi Secretary of State's Office. If the party does not grant him a new election, he can take his case to state court, she said.

A court challenge by McDaniel would likely face an uphill battle, said Matthew Steffey, an election law expert at the Mississippi College School of Law.